Decision analysis is a classical method, which has been well-established over a long period and still is attracting much attention to its importance for coping with the complex decision problems. In particular, the multiobjective extension of this method should be seen in a new light. In a new era of the management, for example, the concept of the value based management (VBM), or the enterprise value creative management, is pervading in the business worlds, which requires to manage the multiobjective point of view properly. The concept of the customer satisfaction (CS) management is also inspired along with the increasing recognition of the customer-perceived value concept (Kotler and Armstrong 2005). The corporate social responsibility (CSR) is increasing its importance in the making-money structure of enterprises. For example, ISO 9000:2000 presents the eight principles for the quality management system, in which the customer focus is regarded as the most basic one. ISO9001:2000 demands to be compatible with the requirements of ISO14001:2004 environmental management systems (EMS). The balanced score card (BSC) also is well known as one of the efficient tools for executing these principles in practice (Kaplan and Norton 1992, 2001; Tanner 2002). In SSME (Service Sciences, Management, and Engineering), which is also recently inspired, a cross disciplinary approach as “research at a crossroads” is stressed and “services is a people business,” and
its “profitability” is raised as its characteristics (e.g Technology Review, special issue on Research in
Development, may 2005, MIT).
In addition, under the increasing versatility in the business environments, the valuation of corporate management is much concerned with the treatment of the uncertainty. Decision analysis has been presented an effective method in using decision tree analysis (Copeland et al. 1995, Copeland and Antikarov 2001, Goodwin and Wright 2004, Koller et. al. 2005). In this context, expected utility theory should be recaptured and its multiobjective extensions are expected. Although the foundations for those developments have already been presented, the operational use of the methods in an integrated form has not yet been developed. For effective operation of this approach, further development in the conceptual construction of an integrated methodology is required, which is an intelligent decision support system with the computer assistance.
This paper has discussed the background of decision analysis and presents an integrated method for its strategic use of multiobjective decision analysis. A new computer program MIDASS has been presented with the method for heuristic construction of the expected multiattribute utility function (EMUF), which can be used as a unified criterion in the corporate management under the uncertainty. As an example, a decision problem for new product development has been presented with illustrations.
There exist still some rooms to be considered in MIDASS.
The expected multiobjective decision analysis presumes the construction of the decision tree with the n-chance forks, where consequences with the multiple attributes occur at each chance fork. MIDASS is used for evaluating EMUF at the nodes of the decision tree structure. EMUF must be embedded in the decision tree structure. Decision analysis, however, usually constructs the decision tree in multiple stages. MIDASS must be used repeatedly at every node in the multi-staged decision tree structure. In this situation, a device for more effective operation of MIDASS will be required, which needs further evolution of the MIDASS program.
(2) In MIDASS, the assignment of DM’s evaluation is made with deterministic values. The evaluation in decision making, however, is ambiguous in twofold: One is the cognitive ambiguousness both in the utility assessment and the probability assessment by DM. Two is the incompleteness of information to be obtained by DM. The assessments for the ambiguity usually are performed with the ambiguous quantities such as fuzzy numbers (Seo 1992, 1997; Nishizaki and Seo 1994) or with the random values such as in the probabilistic utility functions (Luce and Suppes 1965; Seo 2000). The extension of MIDASS to these directions has much academic interest. Even so, however, the effort for these directions will introduce much complexity in the decision support systems, which may sacrifice seriously the user-friendly property in the decision support systems.
MIDASS supports at present the decision ambiguity in three ways.
(i) The thinking processes of DM for the evaluations are constructed sequentially with the interactive assistance not only by the computer, but also by the internal self-examination of DM, in which the evaluation can go back to the preceding steps and revise it repetitively.
(ii) MIDASS includes the Bayes theorem for coping with the ambiguity in the probability evaluation of DM. The use of sample information is included in the decision tree structure (Raiffa 1968, etc.). The acquisition of the sample information, however, is sometimes not realistic for the business decisions environments, in particular, in such the case as the repeated experiments.
(iii) For coping with the decision ambiguity, the construction of decision tree structure at multiple stages is recommended, where the phases for revising the evaluation results can be included.
In further evolution of MIDASS, the development of the method to embed it more effectively and repeatedly in the decision tree structure should be expected. MIDASS presents a first but primal step for this work with the selective and manual operations.
MIDASS software disk is available from the first author on your reruest.
References
Bell, D. E., H. Raiffa and A. Tversky, Descriptive, normative and prescriptive interactions in decision making, in Bell, D. E., H. Raiffa and A. Tversky, Decision Making: Descriptive, Normative and
Prescriptive Interactions: Cambridge University Press, 9-30. 1988.
Copeland, T., T. Koller, and J. Murrin, Valuation: Measuring and Managing the Value of Companies, McKinsey. 2nd ed. 1995.
Copeland, T. and V. Antikarov, Real Options, TEXERE LLC, New York 2001.
Goodwin, P. and G. Wright, Decision Analysis for Management Judgement, 3rd ed. John Wiley, 2004. Kaplan, R. S. and D. P. Norton, The Balanced Scorecard, Measure That Drive Performance,Harvard
Business Review, Jan-Feb. 71-84. 1992.
Kaplan, R. S. and D. P. Norton, The Strategy Focused Organization, Harvard Business School Press. 2001.
Koller, T., M. Goedhart and D. Wessels, Valuation: Measuring and Managing the Value of Companies, McKinsey & Company, Inc. 2005 (4th ed.)
Kotler, P. and G. Armstrong, Principles of Marketing, 11th ed. Prentice Hall. 2006. Keeney, R. L. Multiattribute utility functions. Operations Research, 22. 22-34. 1974.
Keeney, R. L. and H. Raiffa. Decisions with Multiple Objectives, Preferences and Value Tradeoffs. John Willey & Sons. 1976.
Luce, R.D. and H. Raiffa, Games and Decisions, John Wiley & Sons. 1957.
Luce, R. D., and P. Suppes, Preference, utility and subjective probability, in Luce, R. D., R. R. Bush and E. Galanter (eds.) Handbook of Mathematical Psychology, John Wiley. 249-410. 1965. Mesarovic, M.D., D. Macko and Y. Takahara, Theory of Hierarchical, Multilevel, Systems. Academic
Press, New York. 1970.
Meyer, R. F. and J. W. Pratt, The consistent assessment and fairing of preference functions, IEEE
Transactions on Systems Science and Cybernetics, SSC-4, 270-278. 1968.
Nishizaki, I. and F. Seo, Interactive support for fuzzy trade-off evaluation in group decision making,
Fuzzy Set and Systems, 68 309-325. 1994.
Pratt, J. W., Risk aversion in the small and in the large, Economrtrica, vol. 32, 122-136, 1964.
Pratt, J. W., H. Raiffa and R. Schlaifer, Introduction to Statiscal Decision Theory, MIT Press. 1995. (Preliminary edition. McGraw-Hill. 1965.)
Raiffa, H., Decision Analysis, Addition Wesley, Mass. 1968. (Reprinted by Random House, New York.)
Raiffa, H. and R. Schlaifer, Applied Statistical Decision Theory, MIT Press. 1961.
Sakawa, M. and F. Seo. An Interactive Computer Program for Subjective Systems and its Application, WP-80-64. IIASA. Laxenburg. Austria. 1980.
Savage, L. J., The Foundations of Statistics, John Wiley. 1954.
Schlaifer, R., Probability and Statistics for Business Decisions, McGraw-Hill. 1959.
Schlaifer, R., Analysis of Decisions under uncertainty. McGraw-Hill. 1969. (Reprinted by Robert E. Krieger 1978)
Schlaifer, R., Computer Program for Elementary Decision Analysis. Graduate School of Business Administration, Harvard University. 1971.
Seo, F., Fundamentals of intelligent support systems for fuzzy multiobjective decision analysis, in Tzeng, G. H.. H. A. Wang, M. P. Wenn and P. L. Yu (ed.), Multiple Criteria Decision Making, Springer-Verlag, 208-268. 1992.
Seo, F., Construction of fuzzy utility function in group decision making, in Kacprzyk, J., M. Nurmi and M. Fefrizzi (eds.), Consensus under Fuzziness, ed. By Kluwer. 211-230. 1997.
Seo, F., Multiple risk assessment with random utility models in probabilistic group decision making, in
Research and Practice in Multiple Criteria decision Making, Springer, 161-172. 2000.
Seo, F. and I. Nishizaki. A Configuration of intelligent decision support systems. In J. Wessels and A. P. Wierzbicki (eds.), User-Oriented Methodology and Techniques of Decision Analysis and Support. Springer-Verlag. 35-47. 1993.
Seo, F. and I. Nishizaki, On Development of Interactive Decision Analysis Support Systems (IDASS) in the IDSS Environments. Presented paper at the IIASA Workshop on Advances in Methodology and Software for Decision Support Systems. IIASA, Laxenburg, Austria. 1997. (Electronic version).
Seo, F. and M. Sakawa, Multiple Criteria Decision Analysis in Regional Planning: Concepts, Methods
and Applications, D. Reidel Publishing Co. 1988.
Seo, F., M. Sakawa, K. Yamane and T. Fukuchi, Multiobjective systems analysis for impact evaluation of the Hokuriku Shinkansen (Super–express railway), in G. Fandel, M. Grauer, A. Kurzhanski and A. Wierzbicki (eds.), Large Scale Modeling and Interactive Decision Analysis, Springer-Verlag, 314-325. 1986.
Seo, F., I. Nishizaki and S-H. Park. Multiattribute utility analysis using object-oriented programming MAP and its application. Studies on Business Administration and Information 7, 27-57. Setsunan University. 1999.
Sicherman, A. An Interactive Computer Program for Assessing and Using Multiattribute Utility Functions, Technical Report 111. Operations Research Center, MIT. 1975.
von Neumann and O. Morgenstern, Theory of Games and Economic Behavior, Princeton University Press. 1944, 2nd ed.1947.
Tanner, S., Beyond Registration. Getting the Best From ISO9001 and Business Improvement, The European Center for Business Excellence. The British Standard Institution. 2002.
Appendix
A. Instruction for Preference Evaluation (<INSTRUCTION>)
Evaluation for the decreasing risk-averse preferences with the 5 points input method proceeds in following order.
(1) On the evaluation screen first appeared, assign tentatively the input values for three fractiles, 0.25, 0.5, and 0.75. The values for 0.0 and 1.0 points are automatically indicated. MIDASS draws a preference curve for the input data with a click on the <OK> button.
(2) Proceed to the Consistency Check screen with the <NEXT> button. MIDASS checks the consistency of the 5 input points with the decreasing positive risk aversion functions.
(i) Confirm the 50-50 gambles and their certainty equivalent (CE) values for the user sequentially. The 50-50 chance lottery technique is used for the construction or confirmation of the preference curve for the user. The lottery technique assesses a lottery and its certainty equivalent (CE). Three lotteries with the 50-50 chance forks are constructed, whose consequences for the attribute are v(0.0) or v(1.0), v(0.0) or v(0.5), and v(0.5) or v(0.0) and their certainty equivalents (CE) are assessed with 0.5, 0.25, and 0.75-values of the preferences respectively. The three lotteries are constructed with the substitutions of the assessed attribute values in order. Then assign the CE values as input data on the screen.
The v(x.x) denotes the value of an attribute, for which user’s preference is assessed with the x.x-value. Note that the worst value of the attribute is assessed with the 0.0-value of the preference, which is represented as v(0.0), and the best value is assessed with 1.0, which is represented as v(1.0). On the screen, the parenthesis of v(x.x) is omitted.
(ii) Check the input values for CE carefully. Then supply presumably the Assessed value v*(.5) as the same as the Implied value v (.5). (iii) Follow the messages generated by MIDASS. The user can revise the Assessed value v*(.5) on the screen deliberately according to the suggestions.
(3) The user can be back to the first input screen, if necessarily, with a click on the <QUIT> button. Check the shape of the preference curve on the screen, which is newly generated with the revised input values. Then proceed to the Consistency Check screen again with the NEXT button.
(4) This process can be repeated many times until the user is satisfied with the consistency, which is informed by a message on the screen.
(5) When the consistency has been obtained for the decreasing risk aversion, choose the utility function type to be assessed, the piecewise-exponential average type (PIECEX) or the sum-of-exponential type (SUMEX) with the <PIECEXFIT> button or the <SUMEXFIT> button on the screen respectively.
B. Instruction for Selecting the Probability Distribution (<HELP>)
MIDASS supports the derivation of three types of the probability distributions: Continuous probability, Piecewise quadratic distribution, and Discrete distribution. The continuous probability is derived in the mathematical distribution functions, whose input values are assigned by the user. The piecewise quadratic distribution is derived in the piecewise quadratic function forms with the input data assigned by the user. The discrete distribution is constructed with the relative frequency distribution in the histogram and its smoothing represents the piecewise linear distribution functions. MIDASS also supports Bayes statistics.
In the probability evaluation, the ALT-value indicated for the attribute is used as the uncertain quantity. The distribution functions for the uncertain quantities are constructed heuristically by the user. Input data is different according to the distribution types.
The evaluation proceeds with selecting the proper button on the menu screen for the probability evaluation.
I. Continuous Probability Distribution
The evaluation of the continuous distributions are not so much "flexible" due to the use of the mathematical distribution forms, but more "reasonable" and easier to generate and manipulate in the subsequent works.
MIDASS supports three groups of the mathematical distributions. The selection of the distribution type depends on the quantitative characteristics of the data (i.e. the attribute value as an uncertain quantity).
A. Family Group 1, for which the attribute data takes the values between 0 and 1.
B. Family Group 2, for which the attribute data takes the nonnegative values (i.e. larger than 0). C. Family Group 3, for which the attribute data takes the unrestricted values (from minus infinity to plus infinity).
Input data for the assessment are usually parameters, moments, and/or fractiles of the distribution. < General attention! >
(1) Note that the assessor usually has an inclination to assess the 0.25 and 0.75-fractiles with substantially shorter tails than they should be.
(2) The graph on the screen can be enlarged with a click when the numerical values on the horizontal axis are shown with congestion.
A. Family Group 1. Attribute data takes 0 to 1 values.
1. Beta distribution: <Beta>
This type may have a wide variety of shapes and easy to assess by the user. The distribution may be either symmetric or skew depending on the parameters. --- Suggestion ---
The evaluation is recommended in the following process. (1) Try this distribution type first.
(i) Assess the values for the 0.25 and 0.75-fractiles.
(ii) Alternatively, if it is available, input the mean (MEAN), m, and the standard deviation (STDDEV) values as the moments. The MEAN-value must be in between 0 and 1. The STDDEV-value must be in between 0 and Sqrt(m(1 - m)).
(2) When the user is not satisfied with the skewness of the assessed distribution, the parameter adjustment will be helpful for the correction of the skewness.
(i) When the parameter B increases, the distribution skews to the right side having a longer tail to the left side. When the parameter B decreases, the distribution skews to the left-side having a longer tail to the right side.
(ii) When the parameter C increases with the fixed B-value, the variance (dispersion) will become smaller, and vice versa.
<Attention!>
The parameter C should be larger than the parameter B > 0.
2. Bounded lognormal distributions: <Bounded Lognormal>
This family closely resembles the beta distributions, except in the cases when the beta distribution is nearly uniform and when the substantial probability is assigned to the data values very close to 0 or 1.
--- Suggestion ---
(1) When the user is not satisfactory with the beta distribution, try this distribution type. (2) Assess the distribution first with the same fractile values as the beta distribution.
(3) When the distribution shape is not satisfactory to the user, try to change the values of the two fractiles to the same direction, either increase or decrease.
(4) Try, for example, to decrease the values a bit both for the 0.25 and 0.75-fractiles. Then the distribution will skew to the left side. When the fractiles increase, the distribution skews to the right side.
(5) If desired, the parameter values can be corrected on the reference of the values generated by the program.
<Attention!>
B. Family Group 2: Attribute data takes nonnegative values.
This family is applied to most popular data and is used widely. Economic and managerial data have generally nonnegative characteristics.
The user is recommended to proceed in order with the following distribution types.
1. Lognormal distributions: <Lognormal>
The shape of this family is always skew with a long tail to the right side. --- Suggestion ---
(1) Try this distribution type first in this Group. Input the values for the fractiles as indicated. (2) If the spread from the 0.25 to the 0.75-fractile is small relative to the distance between the origin and the median, then the shape of the distribution will be nearly symmetric.
As the spread increases, the distribution becomes more and more skew.
(3) The parameter MU is an unrestricted value and the SIGMA is a positive value.
2. Logstudent distributions: <Logstudent>
The tails of the logstudent may be longer than the tails of the lognormal, but they cannot be shorter. The control over the tail length works only in one direction.
--- Suggestion ---
(1) When the user is not satisfactory with the lognormal distribution, try this distribution type. (2) When you wish to extend both tails longer than in the lognormal distributions, use this type of distribution with the values for the 0.25 and 0.75-fractiles fixed and increase a bit for the 0.875-fractile. The value of the 0.875-fractile for the logstudent may be greater than that of the lognormal distribution, but cannot be smaller.
(3) For the correction of the skewness, the user also can change the parameters, SIGMA for example. When the value increases, the shape skews to left side. When the value decreases, the shape moves to the center position and becomes more close to the symmetric type.
(4) The parameter MU is unrestricted, but SIGMA and NU should take positive values.
3. Gamma-q distributions: <Gamma-q>
When the user wishes to extend one tail longer and shorten the other in the lognormal distribution, use this distribution type with the values for the 0.25 and 0.75-fractiles fixed.
The parameter q controls the length of the tails of the distribution and can be any positive or negative value other than 0.
The program requests the user to specify the parameter q directly as input data. Two additional assignments are either other two parameters or the values for the 0.25 and 0.75-fractiles of the distribution.
--- Suggestion ---
(1) Try first the same values for the 0.25 and 0.75-fractiles as the preceding distribution. (2) Follow the subsequent steps.
Step 1. Start with q = 1 when you wish to extend the left tail, or start with q = - 1 when you wish to extend the right tail.
Step 2. If this shape is not satisfactory to the user, then double or halve the q-values sequentially. As the q-value increases, the shape of the distribution skews to the right side having a longer tail to the left side. As the q-value decreases, the distribution skews to the left side having a longer tail to the right side.
(3) If the parameter q is positive, the left tail is longer and the right tail is shorter than in the lognormal distribution. When the q is negative, the reverse is true.
(4) When the parameter q approaches 0 from either side, the shape of the distribution approaches the lognormal distribution.
(5) The two parameter values, R and S, should be positive. < Attention!>
(1) The q-value should not be set very close to 0.
(2) The values of the fractiles are fixed in the Step 1 and the Step 2.
4. Weibull distributions: <Weibull>
Weibull distribution is used independently to assess the extreme distributions, which is applied to